Question

Let f left parenthesis x right parenthesis equals 4 x plus 9 and g left parenthesis x right parenthesis equals 5 x squared. Perform the function operation and then find the domain of the result.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To perform the function operation, we need to find f(g(x)), which means we plug g(x) into the function f(x).

g(x) = 5x^2
f(g(x)) = f(5x^2)
f(5x^2) = 4(5x^2) + 9
f(5x^2) = 20x^2 + 9

Now, to find the domain of f(g(x)), we need to consider the domain of g(x) first.

Since g(x) = 5x^2 is a polynomial function, its domain is all real numbers. Therefore, we can plug any real number into g(x).

Now, considering the domain of f(g(x)) = 20x^2 + 9, there are no restrictions on the domain of this function. Therefore, the domain of f(g(x)) is all real numbers.